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SimpsonIntegrator (Commons Math 3.2 API)
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org.apache.commons.math3.analysis.integration</FONT>
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Class SimpsonIntegrator</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html" title="class in org.apache.commons.math3.analysis.integration">org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator</A>
      <IMG SRC="../../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.analysis.integration.SimpsonIntegrator</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/UnivariateIntegrator.html" title="interface in org.apache.commons.math3.analysis.integration">UnivariateIntegrator</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public class <B>SimpsonIntegrator</B><DT>extends <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html" title="class in org.apache.commons.math3.analysis.integration">BaseAbstractUnivariateIntegrator</A></DL>
</PRE>

<P>
Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
 Simpson's Rule</a> for integration of real univariate functions. For
 reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
 chapter 3.
 <p>
 This implementation employs the basic trapezoid rule to calculate Simpson's
 rule.</p>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>1.2</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: SimpsonIntegrator.java 1364387 2012-07-22 18:14:11Z tn $</DD>
</DL>
<HR>

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<CODE>static&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SIMPSON_MAX_ITERATIONS_COUNT">SIMPSON_MAX_ITERATIONS_COUNT</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Maximal number of iterations for Simpson.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="fields_inherited_from_class_org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Fields inherited from class org.apache.commons.math3.analysis.integration.<A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html" title="class in org.apache.commons.math3.analysis.integration">BaseAbstractUnivariateIntegrator</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#DEFAULT_ABSOLUTE_ACCURACY">DEFAULT_ABSOLUTE_ACCURACY</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#DEFAULT_MAX_ITERATIONS_COUNT">DEFAULT_MAX_ITERATIONS_COUNT</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#DEFAULT_MIN_ITERATIONS_COUNT">DEFAULT_MIN_ITERATIONS_COUNT</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#DEFAULT_RELATIVE_ACCURACY">DEFAULT_RELATIVE_ACCURACY</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#iterations">iterations</A></CODE></TD>
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<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SimpsonIntegrator()">SimpsonIntegrator</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Construct an integrator with default settings.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SimpsonIntegrator(double, double, int, int)">SimpsonIntegrator</A></B>(double&nbsp;relativeAccuracy,
                  double&nbsp;absoluteAccuracy,
                  int&nbsp;minimalIterationCount,
                  int&nbsp;maximalIterationCount)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a Simpson integrator with given accuracies and iterations counts.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SimpsonIntegrator(int, int)">SimpsonIntegrator</A></B>(int&nbsp;minimalIterationCount,
                  int&nbsp;maximalIterationCount)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a Simpson integrator with given iteration counts.</TD>
</TR>
</TABLE>
&nbsp;
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<CODE>protected &nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#doIntegrate()">doIntegrate</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Method for implementing actual integration algorithms in derived
 classes.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator"><!-- --></A>
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<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.analysis.integration.<A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html" title="class in org.apache.commons.math3.analysis.integration">BaseAbstractUnivariateIntegrator</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#computeObjectiveValue(double)">computeObjectiveValue</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getAbsoluteAccuracy()">getAbsoluteAccuracy</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getEvaluations()">getEvaluations</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getIterations()">getIterations</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getMax()">getMax</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getMaximalIterationCount()">getMaximalIterationCount</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getMin()">getMin</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getMinimalIterationCount()">getMinimalIterationCount</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#getRelativeAccuracy()">getRelativeAccuracy</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#integrate(int, org.apache.commons.math3.analysis.UnivariateFunction, double, double)">integrate</A>, <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#setup(int, org.apache.commons.math3.analysis.UnivariateFunction, double, double)">setup</A></CODE></TD>
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<A NAME="SIMPSON_MAX_ITERATIONS_COUNT"><!-- --></A><H3>
SIMPSON_MAX_ITERATIONS_COUNT</H3>
<PRE>
public static final int <B>SIMPSON_MAX_ITERATIONS_COUNT</B></PRE>
<DL>
<DD>Maximal number of iterations for Simpson.
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../../../constant-values.html#org.apache.commons.math3.analysis.integration.SimpsonIntegrator.SIMPSON_MAX_ITERATIONS_COUNT">Constant Field Values</A></DL>
</DL>

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<A NAME="SimpsonIntegrator(double, double, int, int)"><!-- --></A><H3>
SimpsonIntegrator</H3>
<PRE>
public <B>SimpsonIntegrator</B>(double&nbsp;relativeAccuracy,
                         double&nbsp;absoluteAccuracy,
                         int&nbsp;minimalIterationCount,
                         int&nbsp;maximalIterationCount)
                  throws <A HREF="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</A></PRE>
<DL>
<DD>Build a Simpson integrator with given accuracies and iterations counts.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>relativeAccuracy</CODE> - relative accuracy of the result<DD><CODE>absoluteAccuracy</CODE> - absolute accuracy of the result<DD><CODE>minimalIterationCount</CODE> - minimum number of iterations<DD><CODE>maximalIterationCount</CODE> - maximum number of iterations
 (must be less than or equal to <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SIMPSON_MAX_ITERATIONS_COUNT"><CODE>SIMPSON_MAX_ITERATIONS_COUNT</CODE></A>)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</A></CODE> - if minimal number of iterations
 is not strictly positive
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></CODE> - if maximal number of iterations
 is lesser than or equal to the minimal number of iterations
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</A></CODE> - if maximal number of iterations
 is greater than <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SIMPSON_MAX_ITERATIONS_COUNT"><CODE>SIMPSON_MAX_ITERATIONS_COUNT</CODE></A></DL>
</DL>
<HR>

<A NAME="SimpsonIntegrator(int, int)"><!-- --></A><H3>
SimpsonIntegrator</H3>
<PRE>
public <B>SimpsonIntegrator</B>(int&nbsp;minimalIterationCount,
                         int&nbsp;maximalIterationCount)
                  throws <A HREF="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A>,
                         <A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</A></PRE>
<DL>
<DD>Build a Simpson integrator with given iteration counts.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>minimalIterationCount</CODE> - minimum number of iterations<DD><CODE>maximalIterationCount</CODE> - maximum number of iterations
 (must be less than or equal to <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SIMPSON_MAX_ITERATIONS_COUNT"><CODE>SIMPSON_MAX_ITERATIONS_COUNT</CODE></A>)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</A></CODE> - if minimal number of iterations
 is not strictly positive
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</A></CODE> - if maximal number of iterations
 is lesser than or equal to the minimal number of iterations
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</A></CODE> - if maximal number of iterations
 is greater than <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SIMPSON_MAX_ITERATIONS_COUNT"><CODE>SIMPSON_MAX_ITERATIONS_COUNT</CODE></A></DL>
</DL>
<HR>

<A NAME="SimpsonIntegrator()"><!-- --></A><H3>
SimpsonIntegrator</H3>
<PRE>
public <B>SimpsonIntegrator</B>()</PRE>
<DL>
<DD>Construct an integrator with default settings.
 (max iteration count set to <A HREF="../../../../../../org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html#SIMPSON_MAX_ITERATIONS_COUNT"><CODE>SIMPSON_MAX_ITERATIONS_COUNT</CODE></A>)
<P>
</DL>

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<A NAME="doIntegrate()"><!-- --></A><H3>
doIntegrate</H3>
<PRE>
protected double <B>doIntegrate</B>()
                      throws <A HREF="../../../../../../org/apache/commons/math3/exception/TooManyEvaluationsException.html" title="class in org.apache.commons.math3.exception">TooManyEvaluationsException</A>,
                             <A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Method for implementing actual integration algorithms in derived
 classes.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html#doIntegrate()">doIntegrate</A></CODE> in class <CODE><A HREF="../../../../../../org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.html" title="class in org.apache.commons.math3.analysis.integration">BaseAbstractUnivariateIntegrator</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>the root.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/TooManyEvaluationsException.html" title="class in org.apache.commons.math3.exception">TooManyEvaluationsException</A></CODE> - if the maximal number of evaluations
 is exceeded.
<DD><CODE><A HREF="../../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the maximum iteration count is exceeded
 or the integrator detects convergence problems otherwise</DL>
</DD>
</DL>
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